Quantization of Black Holes Xiao-Gang He1, 2, 3, 4, ∗ and Bo-Qiang Ma1, 2, 4, † 1School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 2Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617 3Institute of Particle Physics and Cosmology, Department of Physics, Shanghai JiaoTong University, Shanghai 200240 4Center for High-Energy Physics, Peking University, Beijing 100871 Abstract We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr’s idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can be also derived from an Ansatz of quantized entropy ∆S = 4πk∆R/λ, which was suggested in a previous work to unify the black hole entropy formula and Verlinde’s conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This suggests a way to unify gravity with quantum theory. Several interesting and surprising results of black holes are given from which we predict the existence of primordial black holes ranging from Planck scale both in size and energy to big ones in size but with low energy behaviors. PACS numbers: 04.70.Dy, 03.67.-a, 04.70.-s, 04.90.+e arXiv:1003.2510v3 [hep-th] 5 Apr 2010 ∗Electronic address:
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[email protected] 1 The quantization of black holes is one of the important issues in physics [1], and there has been no satisfactory solution yet.